Fibrous-ceramic/aerogel composite tiles have been invented to afford combinations of thermal-insulation and mechanical properties superior to those attainable by making tiles of fibrous ceramics alone or aerogels alone. These lightweight tiles can be tailored to a variety of applications that range from insulating cryogenic tanks to protecting spacecraft against re-entry heating. The advantages and disadvantages of fibrous ceramics and aerogels can be summarized as follows: Tiles made of ceramic fibers are known for mechanical strength, toughness, and machinability. Fibrous ceramic tiles are highly effective as thermal insulators in a vacuum. However, undesirably, the porosity of these materials makes them permeable by gases, so that in the presence of air or other gases, convection and gas-phase conduction contribute to the effective thermal conductivity of the tiles. Other disadvantages of the porosity and permeability of fibrous ceramic tiles arise because gases (e.g., water vapor or cryogenic gases) can condense in pores. This condensation contributes to weight, and in the case of cryogenic systems, the heat of condensation undesirably adds to the heat flowing to the objects that one seeks to keep cold. Moreover, there is a risk of explosion associated with vaporization of previously condensed gas upon reheating. Aerogels offer low permeability, low density, and low thermal conductivity, but are mechanically fragile. The basic idea of the present invention is to exploit the best features of fibrous ceramic tiles and aerogels. In a composite tile according to the invention, the fibrous ceramic serves as a matrix that mechanically supports the aerogel, while the aerogel serves as a low-conductivity, low-permeability filling that closes what would otherwise be the open pores of the fibrous ceramic. Because the aerogel eliminates or at least suppresses permeation by gas, gas-phase conduction, and convection, the thermal conductivity of such a composite even at normal atmospheric pressure is not much greater than that of the fibrous ceramic alone in a vacuum.